Multivariate survival distributions of age and residual lifetime processes in nonhomogeneous Poisson process (Q1319146)

Let \(\{N(t), t\geq 0\}\) be the nonhomogeneous Poisson process with cumulative intensity parameter \(\Lambda(t)\), \(\{\delta_ t, t\geq 0\}\) be the age process, and \(\{\gamma_ t, t\geq 0\}\) be the residual lifetime process. Expressions of \(n\)-dimensional survival distribution functions of the processes \(\{\delta_ t\}\) and \(\{\gamma_ t\}\), and their Lebesgue decompositions are derived.